A mathematical model is developed to study the behaviour of an oscillating wave
energy converter in a channel. During recent laboratory tests in a wave tank, peaks
in the hydrodynamic actions on the converter occurred at certain frequencies of the
incident waves. This resonant mechanism is known to be generated by the transverse
sloshing modes of the channel. Here the influence of the channel sloshing modes on
the performance of the device is further investigated. Within the framework of a linear
inviscid potential-flow theory, application of Green’s theorem yields a hypersingular
integral equation for the velocity potential in the fluid domain. The solution is found
in terms of a fast-converging series of Chebyshev polynomials of the second kind.
The physical behaviour of the system is then analysed, showing sensitivity of the
resonant sloshing modes to the geometry of the device, which concurs in increasing
the maximum efficiency. Analytical results are validated with available numerical and
experimental data.